On Characterization of Smarandache Curves Constructed by Modified Orthogonal Frame

Year 2024, Volume: 12 Issue: 3, 101 - 112, 24.09.2024

Kemal Eren , Soley Ersoy

https://doi.org/10.36753/mathenot.1409228

Cited By: 2

Abstract

In this study, we investigate Smarandache curves constructed by a space curve with a modified orthogonal frame. Firstly, the relations between the Frenet frame and the modified orthogonal frame are summarized. Later, the Smarandache curves based on the modified orthogonal frame are obtained. Finally, the tangent, normal, binormal vectors and the curvatures of the Smarandache curves are determined. A special curve known as the Gerono lemniscate curve whose curvature is not differentiable, the principal normal and binormal vectors are discontinuous at zero point is considered as an example, and the Smarandache curves of this curve are obtained by the aid of its modified orthogonal frame, and their graphics are given.

Keywords

Gerono lemniscate curve, Modified orthogonal frame, Smarandache curves

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